MEM 355
Homework 3
1. Set up the following characteristic equations in the form suited to the root locus
method. Be sure to select K so that the numerator and denominator are monic in
each case and the denominator has at least the same order as the numerator
a. versus the parameter
()
1/ 0s
τ
+=
τ
.
b. versus parameter c.
210scsc+++=
c. versus A, versus B, and versus c, if possible. Can a
plot of the of the roots be drawn versus c for given constant values of A
and T by any means at all.
() ( )
310sc ATs++ +=
2. For the characteristic equation
()( )
10
15
K
ss s
+
=
++
Do the followings
a. Draw the real-axis segments of the corresponding root locus.
b. Sketch the asymptotes of the locus for . K→∞
c. For what value of K are the roots on the imaginary axis?
d. Verify your sketch with a MALAB plot.
3. Sketch the root locus with respect to K for the equation
(
)
10KL s
+
= where
()
()
2
1
310
Ls ss s
=++
4. Sketch the root locus with respect to K for the equation
(
)
10KL s
+
= where
() ()
3
3
4
s
Ls ss
+
=
+
5. Sketch the root locus with respect to K for the equation
(
)
10KL s
+
= where
() ()( )
2
2
16
s
Ls ss s
+
=
−+